| 矩阵方程AXB+CX~TD=E自反最佳逼近解的迭代算法 |
| |
| 引用本文： | 杨家稳,孙合明.矩阵方程AXB+CX~TD=E自反最佳逼近解的迭代算法[J].数学杂志,2015,35(5):1275-1286. |
| |
| 作者姓名： | 杨家稳 孙合明 |
| |
| 作者单位： | 滁州职业技术学院基础部, 安徽 滁州 239000,河海大学理学院, 江苏 南京 210098 |
| |
| 基金项目： | 安徽高校省级自然科学基金资助(KJ2011B119) |
| |
| 摘 要： | 本文研究了Sylvester矩阵方程AXB+CXTD=E自反(或反自反)最佳逼近解.利用所提出的共轭方向法的迭代算法,获得了一个结果:不论矩阵方程AXB+CXTD=E是否相容,对于任给初始自反(或反自反)矩阵X1,在有限迭代步内,该算法都能够计算出该矩阵方程的自反(或反自反)最佳逼近解.最后,三个数值例子验证了该算法是有效性的.
|
| 关 键 词： | Sylvester矩阵方程 Kronecker积 共轭方向法 最佳逼近解 自反矩阵 |
| 收稿时间： | 2013/6/12 0:00:00 |
| 修稿时间： | 2013/7/30 0:00:00 |
AN ITERATIVE ALGORITHM FOR THE REFLEXIVE OPTIMAL APPROXIMATION SOLUTION OF MATRIX EQUATIONS AXB + CXTD=E |
| |
| YANG Jia-wen and SUN He-ming.AN ITERATIVE ALGORITHM FOR THE REFLEXIVE OPTIMAL APPROXIMATION SOLUTION OF MATRIX EQUATIONS AXB + CXTD=E[J].Journal of Mathematics,2015,35(5):1275-1286. |
| |
| Authors: | YANG Jia-wen and SUN He-ming |
| |
| Institution: | Department of Basic, Chuzhou Vocational and Technical College, Chuzhou 239000, China and College of Science, Hohai University, Nanjing 210098, China |
| |
| Abstract: | In this paper, we study the optimal approximation solutin of the Sylvester matrix equations AXB + CXTD=E over reflexive (anti-reflexive) matrices. By using the proposed conjugate direction method, we get a result that whatever matrix equations AXB + CXTD=E are consistent or not, for arbitrary initial reflexive (anti-reflexive) matrix X1, the reflexive (anti-reflexive) optimal approximation solution can be obtained within finite iteration steps in the absence of round-off errors. The effectiveness of the proposed algorithm is verified by three numerical examples. |
| |
| Keywords: | sylvester matrix equations Kronecker product conjugate direction method optimal approximation solution reflexive matrix |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《数学杂志》浏览原始摘要信息 |
| 点击此处可从《数学杂志》下载免费的PDF全文 |
